- A−1 and −4
- B1 and −4
- C1 and 4
- D2 and 3
Step-by-Step Solution
Here , so → → → → . Check ; check — both perfect squares. The negative options come from mis-signing the middle term of ; "2 and 3" has the wrong sum and product.
Answer: C) 1 and 4
Find the values of for which has equal roots.
Class 10Quadratic EquationsAlgebra — Quadratics
Key idea: The discriminant — nature of roots
classifies the roots of **: TWO distinct real roots. Parabola crosses -axis at two points.
- ****: ONE repeated real root (called a 'double root' or 'two equal roots'). Parabola touches -axis at the vertex.
- ****: NO real roots. Parabola does not touch the -axis at all.
**Use case**: 'For what values of does have equal roots?' → set → .
You can answer 'how many real roots?' WITHOUT computing them — just compute .
- ****: ONE repeated real root (called a 'double root' or 'two equal roots'). Parabola touches -axis at the vertex.
- ****: NO real roots. Parabola does not touch the -axis at all.
**Use case**: 'For what values of does have equal roots?' → set → .
You can answer 'how many real roots?' WITHOUT computing them — just compute .
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